User contributions for Thakshashila

05:2605:26, 10 June 2025 diff hist +2,674 N Micro F1 Score Created page with "= Micro F1 Score = The '''Micro F1 Score''' is an evaluation metric used primarily in '''multi-class''' and '''multi-label classification''' tasks. Unlike Macro F1 Score, it calculates global counts of true positives, false positives, and false negatives across all classes, then uses these to compute a single Precision, Recall, and F1 Score. It is most useful when the dataset is '''imbalanced''' and you care more about overall performance than per-class fai..."
05:2505:25, 10 June 2025 diff hist +2,699 N Weighted F1 Created page with "= Weighted F1 Score = The '''Weighted F1 Score''' is a metric used in multi-class classification to evaluate model performance by computing the F1 Score for each class and taking the average, weighted by the number of true instances for each class (i.e., the class "support"). It is especially useful when working with '''imbalanced datasets''', where some classes are more frequent than others. == Definition == :<math> \text{Weighted F1} = \sum_{i=1}^{C} w_i \cdot F1_i..."
05:2405:24, 10 June 2025 diff hist +2,380 N Macro F1 Created page with "= Macro F1 Score = The '''Macro F1 Score''' is an evaluation metric used in multi-class classification tasks. It calculates the F1 Score independently for each class and then takes the average (unweighted) across all classes. Unlike the regular F1 Score, which is typically applied to binary classification, the Macro F1 is designed for problems involving more than two classes. == Definition == 1. Compute Precision and Recall for each class individually 2. Compute..."
05:2305:23, 10 June 2025 diff hist +2,994 N Complementary metrics Created page with "= Complementary Metrics in Machine Learning = '''Complementary Metrics''' refer to pairs or groups of evaluation metrics that together provide a more complete and balanced understanding of a classification model’s performance. Because no single metric is perfect, especially in real-world and imbalanced datasets, these metrics are used together to highlight different strengths and weaknesses of a model. == Why Use Complementary Metrics? == Using only one metric like..."
05:2205:22, 10 June 2025 diff hist +2,423 N F1 Score Created page with "= F1 Score = The '''F1 Score''' is a performance metric used in classification problems that balances the trade-off between Precision and Recall (also known as Sensitivity). It is especially useful when the dataset is imbalanced, and both false positives and false negatives are important. == Definition == The F1 Score is the '''harmonic mean''' of Precision and Recall. :<math> F1 = 2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \te..."
05:2205:22, 10 June 2025 diff hist 0 Specificity →Specificity vs Sensitivity
05:2105:21, 10 June 2025 diff hist +2,457 N Specificity Created page with "= Specificity = '''Specificity''', also known as the '''True Negative Rate (TNR)''', is a performance metric in binary classification tasks. It measures the proportion of actual negative instances that are correctly identified by the model. == Definition == :<math> \text{Specificity} = \frac{TN}{TN + FP} </math> Where: * '''TN''' = True Negatives – actual negatives correctly predicted * '''FP''' = False Positives – actual negatives incorrectly predicted as positi..."
05:2005:20, 10 June 2025 diff hist +2,256 N Sensitivity Created page with "= Sensitivity = '''Sensitivity''', also known as '''Recall''' or the '''True Positive Rate (TPR)''', is a performance metric used in classification problems. It measures how well a model can identify actual positive instances. == Definition == :<math> \text{Sensitivity} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – actual positives correctly predicted * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Sensitivit..."
05:2005:20, 10 June 2025 diff hist +2,071 N Accuracy Created page with "= Accuracy = '''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct. == Definition == :<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math> Where: * '''TP''' = True Positives * '''TN''' = True Negatives * '''FP''' = False Positives * '''FN''' = False Negatives Accuracy answers the question: '''"Out of all predict..."
05:1805:18, 10 June 2025 diff hist +4 Recall →Related Metrics
05:1805:18, 10 June 2025 diff hist +1,697 N Recall Created page with "= Recall = '''Recall''' is a metric used in classification to measure how many of the actual positive instances were correctly identified by the model. It is also known as '''sensitivity''' or the '''true positive rate'''. == Definition == :<math> \text{Recall} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – correctly predicted positive instances * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Recall answers th..."
05:1805:18, 10 June 2025 diff hist +1,580 N Precision Created page with "= Precision = '''Precision''' is a metric used in classification tasks to measure how many of the predicted positive results are actually correct. It is also known as the '''positive predictive value'''. == Definition == :<math> \text{Precision} = \frac{TP}{TP + FP} </math> Where: * '''TP''' = True Positives – correct positive predictions * '''FP''' = False Positives – incorrect positive predictions Precision helps to answer the question: '''"Of all the items la..."
05:1805:18, 10 June 2025 diff hist +4 Confusion Matrix →Related Pages
05:1305:13, 10 June 2025 diff hist +2,699 N Confusion Matrix Created page with "= Confusion Matrix = '''Confusion Matrix''' is a performance measurement tool used in machine learning, particularly for classification problems. It provides a summary of prediction results on a classification problem by comparing the actual labels with those predicted by the model. == What is a Confusion Matrix? == A confusion matrix is a table that describes the performance of a classification model. It shows how many instances were correctly or incorrectly predicte..."

04:2504:25, 5 June 2025 diff hist +4 Data Science →Common Techniques current
04:2404:24, 5 June 2025 diff hist +25 Neural Network →Neural Network current
04:2404:24, 5 June 2025 diff hist +25 Data Science →Data Modeling
04:2204:22, 5 June 2025 diff hist +3,974 N Neural Network Created page with "= Neural Network = '''Neural Networks''' are a class of algorithms within Machine Learning and Deep Learning that are designed to recognize patterns. They are inspired by the structure and function of the biological brain and are used to approximate complex functions by learning from data. == Overview == A neural network consists of interconnected units (called '''neurons''' or '''nodes''') organized in layers. These layers process input data through weighted c..."
04:2104:21, 5 June 2025 diff hist +3,619 N Data Science Created page with "= Data Science = '''Data Science''' is an interdisciplinary field that uses scientific methods, algorithms, and systems to extract knowledge and insights from structured and unstructured data. It integrates techniques from statistics, computer science, and domain-specific knowledge to turn raw data into actionable intelligence. == Overview == Data Science combines aspects of data analysis, machine learning, data engineering, and software development to address complex..."
04:2004:20, 5 June 2025 diff hist +3,701 N Deep Learning Created page with "= Deep Learning = '''Deep Learning''' is a subfield of Machine Learning concerned with algorithms inspired by the structure and function of the brain, known as artificial neural networks. It is at the heart of many recent advances in Artificial Intelligence. == Overview == Deep learning models automatically learn representations of data through multiple layers of abstraction. These models excel at recognizing patterns in unstructured data such as images, audio,..." current
04:2004:20, 5 June 2025 diff hist +3,871 N Artificial Intelligence Created page with "= Artificial Intelligence = '''Artificial Intelligence (AI)''' is a branch of computer science that aims to create systems or machines that exhibit behavior typically requiring human intelligence. These behaviors include learning, reasoning, problem-solving, perception, language understanding, and decision-making. == Overview == Artificial Intelligence involves the design and development of algorithms that allow computers and software to perform tasks that would normal..." current
04:1804:18, 5 June 2025 diff hist +2,772 N What is Machine Learning Created page with "= What is Machine Learning = '''Machine Learning (ML)''' is a subfield of artificial intelligence (AI) that focuses on the development of systems that can learn from data and improve their performance over time without being explicitly programmed. == Overview == Machine Learning allows computers to recognize patterns, make decisions, and predict outcomes based on historical data. It contrasts with traditional programming, where rules and logic are manually coded. == T..." current

04:5404:54, 24 May 2025 diff hist +1,102 N Problem: Find (A ∩ B) × (B ∩ C) Created page with "= Problem: Find (A ∩ B) × (B ∩ C) = Given sets: <math>A = \{3, 5, 7\}</math> <math>B = \{7, 8\}</math> <math>C = \{8, 9\}</math> == Step 1: Find the Intersection A ∩ B == Intersection means elements common to both sets. Elements of A: 3, 5, 7 Elements of B: 7, 8 Common element is: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection B ∩ C == Elements of B: 7, 8 Elements of C: 8, 9 Common element is: <math>B \cap C = \{8\}</mat..." current
04:4704:47, 24 May 2025 diff hist +2,182 N Ahmed Zewail Created page with "= Ahmed Zewail - The Father of Femtochemistry = '''Ahmed Hassan Zewail''' (1946–2016) was an Egyptian-American scientist known as the Father of Femtochemistry. He won the '''Nobel Prize in Chemistry''' in 1999 for his pioneering work on observing chemical reactions at extremely fast timescales. == Early Life and Education == * Born in Damanhur, Egypt, in 1946 * Studied at Alexandria University in Egypt * Completed his PhD at the University of Pennsylvania, USA..." current
04:4604:46, 24 May 2025 diff hist +2,397 N Antoine Lavoisier Created page with "= Antoine Lavoisier - The Father of Modern Chemistry = '''Antoine Laurent Lavoisier''' (1743–1794) was a French chemist who is widely regarded as the Father of Modern Chemistry. He revolutionized chemistry by introducing a scientific and quantitative approach to studying matter and chemical reactions. == Early Life and Education == * Born in Paris, France, in 1743 * Educated in science and law, but devoted his life to chemistry * Known for using careful measurem..." current
04:4404:44, 24 May 2025 diff hist +2,428 N Marie Curie Created page with "= Marie Curie - The Pioneer of Radioactivity = '''Marie Curie''' (1867–1934) was a world-renowned scientist known for her groundbreaking work on '''radioactivity'''. She was the first woman to win a Nobel Prize, and the only person to win Nobel Prizes in two different scientific fields — Physics and Chemistry. == Early Life and Education == * Born as '''Maria Sklodowska''' in Warsaw, Poland (1867) * Moved to Paris to study at the University of Paris (Sorbonne)..." current
04:4204:42, 24 May 2025 diff hist 0 Category:Chemistry →Famous Chemists current
04:2904:29, 24 May 2025 diff hist +2,481 N Category:Chemistry Created page with "= What is Chemistry? - Definition, Explanation, and Importance = '''Chemistry''' is the branch of science that studies the '''composition''', '''structure''', '''properties''', and '''changes of matter'''. It helps us understand how substances interact, combine, and change to form new substances. == Definition == Chemistry is the scientific study of: * What matter is made of (elements, atoms, molecules) * How substances behave and interact * How new materials are form..."
04:2804:28, 24 May 2025 diff hist +2,270 N Category:Mathematics Created page with "= What is Mathematics? - Definition, Explanation, and Importance = '''Mathematics''' is the science of numbers, shapes, patterns, and logical reasoning. It helps us solve problems in daily life, science, business, and technology. == Definition == Mathematics is the study of: * '''Numbers''' and their operations (like addition, subtraction) * '''Shapes''' and space (geometry) * '''Patterns''' and sequences (algebra) * '''Measurements''' and quantities * '''Logical thin..." current
04:2704:27, 24 May 2025 diff hist +2,244 N Category:Physics Created page with "= What is Physics? - Definition, Explanation, and Importance = '''Physics''' is the branch of science that deals with the study of the '''natural world''', focusing on the '''matter''', '''energy''', and the '''laws that govern their behavior''. It tries to answer questions like: * How do objects move? * Why do things fall? * What is light? * How is electricity generated? * What causes sound? == Definition == Physics is the scientific study of '''matter''', '''energy..." current
04:2404:24, 24 May 2025 diff hist −8 Cartesian Product →Visual Representation current
04:2404:24, 24 May 2025 diff hist +2,641 N Cartesian Product Created page with "= Cartesian Product - Definition, Explanation, and Examples = The '''Cartesian Product''' is an operation used in mathematics to combine two sets and form a new set made of ordered pairs. This concept is widely used in set theory, coordinate geometry, and computer science. == Definition == If <math>A</math> and <math>B</math> are two sets, the '''Cartesian product''' of <math>A</math> and <math>B</math> is the set of all ordered pairs where: - The first element is fr..."
04:2204:22, 24 May 2025 diff hist −4 Cartesian Product of Two Sets →Cartesian Product of Two Sets - Definition and Step-by-Step Examples current
04:2204:22, 24 May 2025 diff hist −4 Cartesian Product of Two Sets →Cartesian Product of Two Sets - Definition and Step-by-Step Examples
04:2204:22, 24 May 2025 diff hist +2,395 N Cartesian Product of Two Sets Created page with "= Cartesian Product of Two Sets - Definition and Step-by-Step Examples = The [[Cartesian Product]] of two sets is the set of all possible '''ordered pairs''' where the first element comes from the first set and the second element comes from the second set. == Definition == If <math>A</math> and <math>B</math> are two sets, then the Cartesian Product of <math>A</math> and <math>B</math>, denoted by <math>A \times B</math>, is defined as: <math> A \times B..."
04:1804:18, 24 May 2025 diff hist +1,290 N Ordered Pairs in set Created page with "= Ordered Pairs - Definition and Examples = An '''ordered pair''' is a fundamental concept in mathematics used to represent two elements together with an order that matters. It is usually written as <math>(a, b)</math>, where <math>a</math> is called the '''first element''' and <math>b</math> is the '''second element'''. == Key Points == * Unlike sets, the order of elements in an ordered pair is important. * Two ordered pairs <math>(a, b)</math> and <math>(c, d)</ma..." current
04:1604:16, 24 May 2025 diff hist +1,458 N De Morgan Created page with "= Augustus De Morgan - Mathematician Behind De Morgan's Laws = '''Augustus De Morgan''' (1806–1871) was a British mathematician and logician known for his pioneering work in formalizing logic and mathematics. He is famous for formulating the laws that bear his name, called De Morgan's Laws, which are fundamental in set theory, logic, and computer science. == Early Life and Education == - Born in India in 1806, De Morgan moved to England at a young age. - H..." current
04:1504:15, 24 May 2025 diff hist +2,352 N De Morgan’s Laws Created page with "= De Morgan's Laws - Definition, Explanation, and Examples = '''De Morgan''''s laws are fundamental rules in set theory that describe the relationship between union, intersection, and complements of sets. They help simplify complex set expressions, especially involving complements. == Statements of De Morgan's Laws == Let <math>A</math> and <math>B</math> be two sets and <math>U</math> be the universal set. 1. The complement of the union of two sets is equal to t..." current
04:0704:07, 24 May 2025 diff hist +2,665 N Distributive Law of Sets Created page with "= Distributive Law of Sets - Definition, Explanation, and Examples = The '''distributive law''' shows how union and intersection operations distribute over each other. It is a key property in set theory that helps simplify expressions involving both operations. == Distributive Law of Intersection over Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> A \cap (B \cup C) = (A \cap B) \cup (A \cap C) </math> This means the intersecti..." current
03:5503:55, 24 May 2025 diff hist +2,423 N Associative Law of Sets Created page with "= Associative Law of Sets - Definition, Explanation, and Examples = The '''associative law''' is a fundamental property of set operations which states that when performing the same operation multiple times, the grouping (or association) of sets does not affect the result. == Associative Law for Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> (A \cup B) \cup C = A \cup (B \cup C) </math> This means that whether you first unite <..." current
03:4703:47, 24 May 2025 diff hist +1,666 N Commutative law on sets Created page with "= Commutative Law of Sets - Definition, Explanation, and Examples = The '''commutative law''' is an important property of some set operations, meaning the order in which we perform the operation does not affect the result. == Commutative Law for Union == For any two sets <math>A</math> and <math>B</math>, the union operation is commutative. This means: <math> A \cup B = B \cup A </math> In words, combining set <math>A</math> with set <math>B</math> is the same as co..." current
03:4603:46, 24 May 2025 diff hist +3,299 N Complement of a Set Created page with "= Complement of a Set - Definition, Explanation, and Examples = The '''complement''' of a set contains all elements that are not in the set but belong to a larger, universal set. It helps identify what is "outside" a given set within a specified context. == Definition of Complement == Let <math>U</math> be the universal set, which contains all elements under consideration. The complement of a set <math>A</math>, denoted by <math>A'</math> or <math>\overline{A}</math>,..." current
03:4503:45, 24 May 2025 diff hist +2,523 N Difference of Sets Created page with "= Difference of Sets - Definition, Explanation, and Examples = The '''difference''' of two sets is an operation that finds elements that belong to one set but not the other. It is also called the '''relative complement'''. == Definition of Difference == The difference of sets <math>A</math> and <math>B</math>, denoted by <math>A - B</math>, is the set of all elements that are in <math>A</math> but not in <math>B</math>. Mathematically: <math>A - B = \{ x : x \in A \..." current
03:4403:44, 24 May 2025 diff hist +2,287 N Intersection of Sets Created page with "= Intersection of Sets - Definition, Explanation, and Examples = The '''intersection''' of two sets is an important set operation that finds all elements common to both sets. == Definition of Intersection == The intersection of two sets <math>A</math> and <math>B</math> is the set containing all elements that are in both <math>A</math> and <math>B</math>. It is denoted by: <math>A \cap B</math> Mathematically: <math>A \cap B = \{ x : x \in A \text{ and } x \in B \}..." current
03:4303:43, 24 May 2025 diff hist +2,662 N Union of Sets Created page with "= Union of Sets - Definition, Explanation, and Examples = The '''union''' of two sets is a fundamental operation in set theory. It combines all the elements from both sets into one set without repeating any element. == Definition of Union == The union of two sets <math>A</math> and <math>B</math> is the set containing all elements that belong to either <math>A</math>, or <math>B</math>, or both. It is denoted by: <math>A \cup B</math> Mathematically: <math>A \cup B..." current
03:4203:42, 24 May 2025 diff hist +1,772 N Operations on sets Created page with "= Operations on Sets - Overview and Basic Definitions = '''Operations on sets''' are procedures that combine or modify sets to form new sets. They are fundamental in set theory and are widely used in mathematics, computer science, and logic. == Basic Set Operations == Here are the most common operations on sets with brief explanations: * '''Union (∪)''': The union of two sets <math>A</math> and <math>B</math> is the set of all elements that are in <math>A</math> or..." current
03:4003:40, 24 May 2025 diff hist +2,183 N Universal set Created page with "= Universal Set - Definition and Examples = In set theory, the '''universal set''' is the set that contains '''all possible elements''' under consideration for a particular discussion or problem. It serves as the '''reference set''' or '''universe''' of discourse. == Definition of Universal Set == The '''universal set''' is usually denoted by <math>U</math>. It contains every element relevant to the context or subject being studied. For example, if we are discussing..." current
03:3803:38, 24 May 2025 diff hist +2,310 N Proper subset Created page with "= Proper Subset - Definition and Examples = A '''proper subset''' is a special kind of subset where all elements of one set are contained in another set, but the two sets are not equal. In other words, the proper subset must have fewer elements than the original set. == Definition of Proper Subset == A set <math>A</math> is called a '''proper subset''' of a set <math>B</math> if: * Every element of <math>A</math> is in <math>B</math>, and * <math>A</math> is not equa..." current
03:3703:37, 24 May 2025 diff hist +2,590 N Subsets Created page with "= Subsets - Definition, Types, and Examples = In set theory, a '''subset''' is a set whose elements all belong to another set. Subsets are fundamental in understanding the relationships between sets. == Definition of Subset == A set <math>A</math> is called a '''subset''' of a set <math>B</math> if every element of <math>A</math> is also an element of <math>B</math>. This is written as: <math>A \subseteq B</math> This means: <math>\forall x (x \in A \Rightarrow x \i..." current
03:3503:35, 24 May 2025 diff hist +138 Equal Sets →Example 3: current

User contributions for Thakshashila

10 June 2025

5 June 2025

24 May 2025